Numerical Grid Research Articles

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term.

We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach's effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latter─from 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work.

Translating pumping test data into groundwater model parameters: a workflow to reveal aquifer heterogeneities and implications in regional model parameterization

Groundwater modelers frequently grapple with the challenge of integrating aquifer test interpretations into parameters used by regional models. This task is complicated by issues of upscaling, data assimilation, and the need to assign prior probability distributions to numerical model parameters in order to support model predictive uncertainty analysis. To address this, we introduce a new framework that bridges the significant scale differences between aquifer tests and regional models. This framework also accounts for loss of original datasets and the heterogeneous nature of geological media in which aquifer testing often takes place. Using a fine numerical grid, the aquifer test is reproduced in a way that allows stochastic representation of site hydraulic properties at an arbitrary level of complexity. Data space inversion is then used to endow regional model cells with upscaled, aquifer-test-constrained realizations of numerical model properties. An example application demonstrates that assimilation of historical pumping test interpretations in this manner can be done relatively quickly. Furthermore, the assimilation process has the potential to significantly influence the posterior means of decision-pertinent model predictions. However, for the examples that we discuss, posterior predictive uncertainties do not undergo significant reduction. These results highlight the need for further research.

Statistics of detonation confinement: 1D, 2D and 3D simulations in hydrogen–oxygen

Statistical analysis of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) detonation simulations is performed to understand the role of confinement on detonation frontal velocity and thermodynamic states. Simulations considered include a 2D wide channel (5 detonation cells across), a 2D narrow channel (1.5 cells across), a 3D square channel (10 cells around perimeter), and a 3D round tube (6 cells around perimeter), with identical mixture conditions of stoichiometric hydrogen–oxygen with 3000 parts per million by volume (PPMv) ozone at 300 K and 15 kPa. 1D and 2D simulations with the same mixture without ozone are also considered. All simulations solve the compressible Navier–Stokes equations with detailed chemistry and exhibit good agreement with macroscopic characteristics of experiments (e.g., cell size). Results show that the frontal velocity in 3D simulations is more irregular as compared to the 2D simulations, which are more irregular compared to the 1D simulations. The irregularity in frontal velocity leads to broader distributions of shock velocities and shock decay behavior. The 3D simulations also exhibit a wider and more extreme set of thermodynamic states as compared to the 2D simulations immediately behind the shock wave, within the induction zone, and throughout the rest of the domain. Increasing relative boundary losses leads to quantitative differences in both thermodynamic state and frontal velocity, consistent with 1D steady models of detonation with losses. The conclusions drawn in this work are not sensitive to numerical grid resolution.

Quantification and visualization of US racial geography using the National Racial Geography Dataset 2020.

Racial geography studies the spatial distributions of multiracial populations. Technical challenges arise from the fact that US Census data, upon which all US-based studies rely, is only available in the form of spatial aggregates at a few levels of granularity. This negatively affects spatial analysis and, consequently, the quantification of racial segregation, especially on a smaller length scale. A recent methodology called the Racial Landscape (RL) stochastically disaggregates racial data at the level of census block aggregates into a grid of monoracial cells. RL-transformed racial data makes possible pattern-based, zoneless analysis, and visualization of racial geography. Here, we introduce the National Racial Geography Dataset 2020 (NRGD2020)-a collection of RL-based grids calculated from the 2020 census data and covering the entire conterminous US. It includes a virtual image layer for a bird's-eye-like view visualization of the spatial distribution of racial sub-populations, numerical grids for calculating racial diversity and segregation within user-defined regions, and precalculated maps of racial diversity and segregation on various length scales. NRGD2020 aims to facilitate and extend spatial analyses of racial geography and to make it more interpretable by tightly integrating quantitative analysis with visualization (mapping).

Multi-fidelity Kriging extrapolation together with CFD for the design of the cross-section of a falling lifeboat

Surrogate modelling techniques such as Kriging are a popular means for cheaply emulating the response of expensive Computational Fluid Dynamics (CFD) simulations. These surrogate models are often used for exploring a parameterised design space and identifying optimal designs. Multi-fidelity Kriging extends the methodology to incorporate data of variable accuracy and costs to create a more effective surrogate. This work recognises that the grid convergence property of CFD solvers is currently an unused source of information and presents a novel method that, by leveraging the data structure implied by grid convergence, could further improve the performance of the surrogate model and the corresponding optimisation process. Grid convergence states that the simulation solution converges to the true simulation solution as the numerical grid is refined. The proposed method is tested with realistic multi-fidelity data acquired with CFD simulations. The performance of the surrogate model is comparable to an existing method, and likely more robust. More research is needed to explore the full potential of the proposed method. Code has been made available online at https://github.com/robertwenink/MFK-Extrapolation.

Moving iso-contour method for solving partial differential equations

The numerical solution of partial differential equations is often performed on a numerical grid, where the grid points are used for estimating the partial derivatives. The grid can be fully static as in Eulerian type of solution method, or the grid points can move during the solution, which is the case in Lagrangian type of method. In the current article, a numerical solution method is presented, where the grid points are located on iso-contours of the two-dimensional field. The method calculates the local movement of the iso-contours according to an evolution equation described by the PDE, and the solution proceeds by moving the grid points towards the calculated direction. Additional stability is obtained by setting the grid points to move along the iso-contour line. To exemplify the application of the method, numerical examples are calculated for the two-dimensional diffusion equation.

AvaFrame com1DFA (v1.3): a thickness-integrated computational avalanche module – theory, numerics, and testing

Abstract. Simulation tools are important to investigate and predict mobility and the destructive potential of gravitational mass flows (e.g., snow avalanches). AvaFrame – the open avalanche framework – offers well-established computational modeling approaches, tools for data handling and analysis, and ready-to-use modules for evaluation and testing. This paper presents the theoretical background, derivation, and model verification for one of AvaFrame's core modules, the thickness-integrated computational model for avalanches with flow or mixed form of movement, named com1DFA. Particular emphasis within the description of the utilized numerical particle–grid method is given to the computation of spatial gradients and the accurate implementation of driving and resisting forces. The implemented method allows us to provide a time–space criterion connecting the numerical particles, grid, and time discretization. The convergence and robustness of the numerical implementation is checked with respect to the spatiotemporal evolution of the flow variables using tests with a known analytical solution. In addition, we present a new test for verifying the accuracy of the numerical simulation in terms of runout (angle and distance). This test is derived from the total energy balance along the center-of-mass path of the avalanche. This article, particularly in combination with the code availability (open-source code repository) and detailed online documentation provides a description of an extendable framework for modeling and verification of avalanche simulation tools.

A Hybrid Physical Co-Simulation Smart Grid Testbed for Testing and Impact Analysis of Cyber-Attacks on Power Systems: Framework and Attack Scenarios

With the deployment of numerous innovative smart grid technologies in modern power systems, more real-time communication and control are required due to the complexity and proliferation of grid-connected systems, making a power system a typical cyber-physical system (CPS). However, these systems are also exposed to new cyber vulnerabilities. Therefore, understanding the intricate interplay between the cyber and physical domains and the potential effects on the power system of successful attacks is essential. For cybersecurity experimentation and impact analysis, developing a comprehensive testbed is needed. This paper presents a state-of-the-art Hybrid Physical Co-simulation SG testbed at FIU developed for in-depth studies on the impact of communication system latency and failures, physical events, and cyber-attacks on the grid. The Hybrid SGTB is designed to take full advantage of the benefits of both co-simulation-based and physical-based testbeds. Based on this testbed, various attack strategies are tested, including man-in-the-middle (MitM), denial-of-service (DoS), data manipulation (DM), and setting tampering (change) on various power system topologies to analyze their impacts on grid stability, power flow, and protection reliability. Our research, which is based on extensive testing on several testbeds, shows that using hybrid testbeds is justified as both practical and effective.

Realistic turbulent inflow conditions for estimating the performance of a floating wind turbine

Abstract. A novel method for generating turbulent inflow boundary conditions for aeroelastic computations is proposed, based on interfacing hybrid hot-wire and particle image velocimetry measurements performed in a wind tunnel to a full-scale load simulation conducted with FAST. This approach is based on the use of proper orthogonal decomposition (POD) to interpolate and extrapolate the experimental data onto the numerical grid. The temporal dynamics of the temporal POD coefficients is driven by the high-frequency hot-wire measurements used as input for a lower-order model built using a multi-time-delay linear stochastic estimation (LSE) approach. Being directly extracted from the data, the generated three-component velocity fields later used as inlet conditions present correct one- and two-point spatial statistics and realistic temporal dynamics. Wind tunnel measurements are performed at a scale of 1:750, using a properly scaled porous disk as a floating wind turbine model. The motions of the platform are imposed by a linear actuator. Between all 6 degrees of freedom (DOFs) possible, the present study focus on the streamwise direction motion of the model (surge motion). The POD analysis of the flow, with or without considering the presence of the surge motion of the model, shows that a few modes are able to capture the characteristics of the most energetic flow structures and the main features of the wind turbine wake, such as its meandering and the influence of the surge motion. The interfacing method is first tested to estimate the performance of a wind turbine in an offshore boundary layer and then those of a wind turbine immersed in the wake of an upstream wind turbine subjected to a sinusoidal surge motion. Results are also compared to those obtained using the standard inflow generation method provided by TurbSim available in FAST.

RelSIM: A Relativistic Semi-implicit Method for Particle-in-cell Simulations

We present a novel Relativistic Semi-Implicit Method (RelSIM) for particle-in-cell (PIC) simulations of astrophysical plasmas, implemented in a code framework ready for production runs. While explicit PIC methods have gained widespread recognition in the astrophysical community as a reliable tool to simulate plasma phenomena, implicit methods have been seldom explored. This is partly due to the lack of a reliable relativistic implicit PIC formulation that is applicable to state-of-the-art simulations. We propose the RelSIM to fill this gap: our new method is relatively simple, being free of nonlinear iterations and only requiring a global linear solve of the field equations. With a set of one- and two-dimensional tests, we demonstrate that the RelSIM produces more accurate results with much smaller numerical errors in the total energy than standard explicit PIC, in particular when characteristic plasma scales (skin depth and plasma frequency) are heavily underresolved on the numerical grid. By construction, the RelSIM also performs much better than the relativistic implicit-moment method, originally proposed for semi-implicit PIC simulations in the relativistic regime. Our results are promising to conduct large-scale (in terms of duration and domain size) PIC simulations of astrophysical plasmas, potentially reaching physical regimes inaccessible by standard explicit PIC codes.

Simplifying Rogowski Coil Modeling: Simulation and Experimental Verification.

The integration of renewable energy sources, electric vehicles, and other electrical assets has introduced complexities in monitoring and controlling power networks. Consequently, numerous grid nodes have been equipped with sensors and complex measurement systems to enhance network observability. Additionally, real-time power network simulators have become crucial tools for predicting and estimating the behavior of electrical quantities at different network components, such as nodes, branches, and assets. In this paper, a new user-friendly model for Rogowski coils is presented and validated. The model's simplicity stems from utilizing information solely from the Rogowski coil datasheet. By establishing the input/output relationship, the output of the Rogowski coil is obtained. The effectiveness and accuracy of the proposed model are tested using both simulations and commercially available Rogowski coils. The results confirm that the model is simple, accurate, and easily implementable in various simulation environments for a wide range of applications and purposes.

Geological controls of discharge variability in the Thames Basin, UK from cross-spectral analyses: Observations versus modelling

Geological factors controlling daily- to multi-year discharge variability in 48 sub-catchments spanning 10–1000 km2 in the Thames Basin were investigated using cross-spectral analysis. The analyses represent a ‘transfer function approach’ applied to daily observed streamflow (output) versus catchment-wide precipitation (input) for data spanning 1990–2014. Catchments dominated by high-permeability bedrock have significant attenuation of high-frequency precipitation variability and large delays at all frequencies with streamflow dominated by baseflow (high lag1 autocorrelation and high Base Flow Index, BFI). Catchments dominated by low-permeability rocks have little high-frequency attenuation and small delays and consequently ‘flashy’ behaviour. For all sub-catchments >300 km2 in the Thames Basin, attenuation of the highest frequency precipitation variability caused by mixing of flow from upstream plus groundwater flow (representing ‘older’ variability) with direct surface flow (‘younger’ variability) constitutes real-world moving averaging as indicated by a roll-off in power at the highest frequencies.The success of the JULES land surface model in simulating discharge (i.e. surface and sub-surface runoff routed between grid boxes) is also linked to the underlying geology. Larger catchments (>300 km2) are modelled well because routing between numerous grid boxes leads to moving averaging that is a good analogue for the observations. Modelling was least successful (e.g. lowest Kling-Gupta Efficiency) for small catchments (<300 km2) dominated by high-permeability bedrock - with far too little attenuation of high-frequency precipitation variability and insufficient delays at all frequencies. Experimentally switching the soil saturated hydraulic conductivity to that of the underlying bedrock for grid boxes dominated by aquifers significantly improves modelled discharge variability in small sub-catchments - confirming the importance of bedrock permeability in modelling.For small catchments in data-sparse regions, knowledge of the relative proportions of different hydrogeological units (aquifers, aquitards) potentially could be used to predict and model discharge variability as characterised by BFI and lag1 autocorrelation.

Analysis of shift in discharge coefficient for contaminated multihole orifice flow meter

The aim of this paper is to provide a comprehensive numerical study of influence of contamination and multi-hole orifice (MHO) flow meter geometry on shift in discharge coefficient. In this research, authors analyzed steady, three-dimensional, turbulent flow of dry air through MHO flow meter with 3 different β parameters. Shift in discharge coefficient was calculated for 29 different combinations of contamination parameters for 7 contamination angles, 3 different Reynolds numbers and 3 β parameters. Numerical method that was used was finite volume method with SIMPLE algorithm and standard k-ε turbulence model. Grid sensitivity study was performed on four systematically refined numerical grids for MHO with contamination for all values of Reynolds number, all values of β parameters and 3 values of contamination angle. Obtained results were grid independent. Numerical results for MHO without contamination were compared with the experimental results found in the literature. It was found that contamination angle has most influence on shift in discharge coefficient. Also it was found that the contamination has influence on the change of pressure drop values, which directly affects the change of other parameters. Pressure drop and singular pressure loss coefficient of the orifice with contamination are smaller compared to the values for a pure orifice, whereby the measurement accuracy was reduced. It was found that the multi-hole orifice meter was less sensitive to the pressure drop changes due to the increasing of contamination angle in regards to the single-hole orifice meters.

Implementing the slice method to evaluate lateral pile capacity in cohesive soil

AbstractThis paper presents a novel method for evaluating the resistance factor used for the estimation of lateral pile capacity in cohesive soil. The developed method uses limit equilibrium and mobilized strength principles, which are implemented on the half‐symmetric problem using a modification of the traditional slice method. The soil medium is discretized into a polar numerical grid, allowing sliplines investigation independently of geometrical shape assumptions. The paper presents the development of the SLIP (Snake Locomotion Iterative Procedure) optimization method, which enables an effective and efficient search of the critical slipline out of all slipline geometries that can be generated within the numerical grid. The SLIP iteratively updates the evaluated optimal slipline, according to the criterion of minimizing the pile resistance factor, N. The obtained solutions are consistent with previous plasticity results, with special attention to the smooth pile solution which is bounded between the best lower‐ and upper‐bounds solutions to date. The work utilizes safety map principles to prove the uniqueness of the solution.

Analytical Solution for One-Dimensional Transient Thermal Conduction in a Hollow Cylinder

The primary use of analytical solutions in the area of thermal conduction problems is for verification purposes, comparing the calculated temperatures and heat flux values to the results from numerical codes. The contribution from the analytical solutions can be especially significant where large temperature gradients are found. This is because the temperature and heat flux results can be found very precisely: normally to eight or 10 significant figures using analytical solutions. Normally, numerical solutions require extremely fine grids in high-heat-flux locations, but analytical solutions can provide insight into the adequacy of grid densities in these types of situations. One area of particular interest is in nonrectangular analytical solutions because generalized numerical grids do not naturally lend themselves well to curved surfaces without a large number of nodes. In this current study, four solutions are offered in a geometry involving a hollow cylinder. Two of the solutions examine heating from the inside of the cylinder, and two involve heating from the outside. Development of the solutions is provided along with results that show the temperature responses to the various sets of boundary conditions. A mathematical identity is used as part of the solution, which eliminates the need to evaluate an infinite series, along with need to find roots of transcendental equations and evaluate Bessel functions. Intrinsic verification is also applied in order to provide assurance that the solutions are properly formulated and evaluated.

Global Stability Analysis of Full-Aircraft Transonic Buffet at Flight Reynolds Numbers

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier–Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft.

A Multi-Objective Time – Series Optimization for Optimum Planning Design of Integrative Power System with the Effects of Multi-Dimensional Sources of Uncertainty

Time series aggregation (TSA) procedures are used to simplify data entry and enhance solution efficiency. This study suggested a two-step multi-objective optimization framework for TSA strategy determination. TSA methodologies for optimum MES design and operation were used to create the multi-energy system’s preliminary design. In the second step, the system’s total annual cost, as well as loss of load probability (LSLP), were used as objectives, or the optimal combination of the several objectives was found optimal TSA strategy for the MES’s structure and performance. The ideal energy-storage MES design proved the method’s efficacy. TSA techniques were compared and analyzed for architectural schemes & system performance variations. The findings show that the initial full-time series data may be used to verify the viability of the best MES design schemes and quantify the departure of outcomes from alternative TSA procedures. LSLP decrease raises expenses. The TAC of the framework improves from $9.79 × 107 to $1.56 × 108 when the LSLP reduces to 7.90% to zero in the numerous grids method (TG1) with 730-time steps (TS). To fulfill energy system demand, the minimal LSLP approach must be chosen. The best TSA tactics for MES design may be chosen based on unique needs.

Brazilin: An updated literature-based review on its promising therapeutic approaches and toxicological studies

Brazilin is a promising natural red dye, extracted from the wood of Caesalpinia sappan L. It exhibits several pharmacological activities including anti-inflammatory, antioxidant, anti-depressant and anxiolytic, anti-diabetic, anticancer, antibacterial, and vasorelaxant. Moreover, bioavailability studies demonstrated that brazilin is quickly absorbed into the bloodstream. The data were collected from several databases as ScienceDirect, Web of Science, Pubmed and Proquest. This review is designed to conduct an in-depth search on its pharmacological activities, as well as the underlying cell signaling pathways and mechanism of actions. In addition, we have addressed the bioavailability and structural analysis of brazilin and its close derivatives, safety and quality profiles, and toxicological status. Brazilin with its safety characteristics and acceptable bioavailability, has the potential to touch numerous natural grids, thus, it is possible that this medicinally effective molecule will assist as a promising principal for the development of drug in management of different disorders.

Fostering the consensus: a BERT-based Multi-label Text Classifier to support agreement in public design call for tenders

Natural Language Processing (NLP) is a branch of Artificial Intelligence (AI) concerned with allowing computers to process natural human language. NLP is applied to solve several tasks in the design and construction process. However, in scientific literature, no applications are related to the pre-design phase and the processing of quality objectives and needs. The pre-design phase aims to reach a consensus between the stakeholders' quality demands and the design solution, relying on written natural language. Human language is the most pervasive and richest form of human knowledge representation and communication; however, at the same time, it is ambiguous, prone to misinterpretations, and hardly machine computable. Moreover, the mandatory procedural steps of the public tender procedure exacerbate the risk of misinterpretations inherent in using natural language. The study provides a methodology to design, assess, and evaluate an NLP tool based on the latest language model (i.e., BERT) to translate quality demands sentences into an evaluation grid in the Italian public tender context. The methodology is validated against a case study of an educational facility tender. The first results show good accuracy and capability of the NLP system to translate natural language into a numerical grid to support communication and foster consensus among actors, clarifying the appointing party and end-user's objectives to be reached via the design proposals.

A unified multi-step wind speed forecasting framework based on numerical weather prediction grids and wind farm monitoring data

Wind speed forecasting is the basis of wind farm operation, which provides a reference for the future operation status evaluation of wind farms. For the wind speed forecast of wind turbines in the whole wind farm, a strategy combining unified forecast and single site error correction is proposed in this paper. The unified forecast framework is composed of a unified forecast model and multiple single site error correction models, which combines the forecasted grids of numerical weather prediction (NWP) with the monitoring data of wind farms. The proposed unified forecast model is called spatiotemporal conversion deep predictive network (STC-DPN), which is composed of temporal convolution network (TCN) and 2D convolution long short-term memory network (ConvLSTM). Firstly, the NWP forecasted grids are interpolated to the fan location, and the sequence matrix is composed of the NWP data and the monitored data of each wind turbine according to the time series, which is entered into the TCN network for time sequence feature extraction. Then, the output of the TCN network is converted into a regular spatio-temporal data matrix, which is entered into the ConvLSTM network for joint learning of spatio-temporal features to obtain the wind speed sequence forecasted in the whole wind farm. Finally, an independent TCN-LSTM error correction model is added for each site. Variational modal decomposition (VMD) is used to process data series, and different processing methods are adopted in unified forecast and single site error correction. In the 96 steps forecast test of a wind farm from Jining City, China, the proposed method is superior to several baseline methods and has important practical application value.